The re-election of numerous Republican governors—and the expansion of Republican control into deep blue territory—signals that voters will back policy makers who tackle contentious issues like welfare reform, labor policy, and spending cuts, potentially helping shape the national GOP agenda.

Govs. Rick Snyder of Michigan, Scott Walker of Wisconsin, Rick Scott of Florida, Sam Brownback of Kansas, and Paul LePage of Maine were thought to be vulnerable, in part because of economic policies they pursued in their states since 2011....